Calculus and Aviation Applications

Lectures by Dr. Steven Holding

College of Aeronautical Science

Curriculum Overview

The curriculum combines standard year 12 Algebra and Calculus with applications in Flight Principles, Flight Planning and Aviation related topics. The student is thus encouraged to learn new concepts by way of illustrations in a familiar and useful area.

The Aeronautical Mathematics Curriculum (Year 12) is approved for the educational requirements for pilots/ cadets entering into all major Australian Airlines. The certificate obtained also meets the educational requirement for ADF Pilot, Air Crew or Officer(Army, Navy and Airforce) entry.  The course can also be used as a Mathematics prerequisite for entry into Griffith University Bachelor of Aviation or any science based university course. Here is the link to the Griffith University web page – Griffith university – Aviation management.

Lecture Format and Home Study Requirements

The lecture material is presented during a 4 week period (Monday to Friday). The course can be attended either full time or part correspondence.

Small class size (maximum of 12) allows individual assistance during formal lecture time. Individual tutorials are available upon request (no extra fee for this service).


Two exams are given, comprising 30% (2 hours duration) and 70% (3 hours duration) of the final mark. Assignments are a compulsory component (no mark allocation). The minimum requirement to achieve a pass level is an overall result of 60%. The student’s exam result, as a percentage will be recorded on the certificate. Exam dates can be adjusted to suit student schedules or work commitments. Students requiring extra study time may elect to delay the scheduled exam date.

Research and Extended Curriculum

Course material naturally evolves with time. As new aircraft types are developed, illustrative aspects of the aircraft’s performance may be included in lecture material. Examples may be varied to include familiar aircraft, or those of particular interest to the student. The Standardized Drag Curve© and associated results were specifically developed for this course as a teaching aid.

Brief Course Outline

Core Topics:

  • Algebra
  • Functions
  • Graph Plotting
  • Maxima, Minima, Critical Points
  • Polynomials
  • Reciprocal Functions
  • Exponential and Natural Log Functions
  • Derivatives
  • Integration
  • Modeling Physical Systems
  • Probability

Special Topics:

  • Takeoff and Landing Distance
  • Climb Performance Calculations
  • Lift Formula
  • Effect of Altitude upon Performance
  • Analysis of the Standardized Drag Equation©
  • Applications of Calculus in Optimizing Aircraft Performance Includes:
    • Calculations for Speed of Sound and Mach Number
    • Stall Speed
    • Absolute Ceiling
    • Service Ceiling
    • Minimum Drag Speed
    • Best Angle of Climb
    • Best Rate of Climb
    • Best Endurance Speed
    • Best Range Speed
    • Maximum Cruise Speed (Thrust Limited)
    • Fuel Flow and Range Equations

Course Preparation

The minimum commencement level is Year 10 in advanced level Mathematics. Pre-course study is recommended for all students.

Preparation Study: The following text gives a good overview of the basics. “MATHEMATICS FOR AUSTRALIA 10A (advanced)”. The text can be ordered direct from the publisher. Haese Mathematics, PO Box 38, Adelaide Airport, SA, 5950, Phone 08-83559444.To order go to; Please email me to obtain the relevant Chapters and Sections of the text. Topics covered in the text are Metric Units, Trigonometry, Algebra, Formula and Equations. I suggest that you first attempt the revision questions at the end of each chapter. Note that this material will be revised in the first week of the lecture course. Please email Dr Steven Holding if you need any assistance.



The aim is to present the standard Year 12 introduction to Calculus with emphasis on applications in Flight Theory and Aeronautical Engineering. I feel that the students benefit greatly from the inclusion of relevant material, individual tuition, and my enthusiasm for the subject. The present lecture material is the accumulated results of 25 years of teaching in the field as well as teaching and research experience at University level.


The Enrollment form can be downloaded here

Course Venue

Brisbane: Saint Johns College, College Rd, Saint Lucia. (on University of Queensland Campus)

Cost / Schedule

Please contact Dr. Steven Holding for course fees and current lecture schedules.
mobile 042 303 7474


Accommodation (including all meals) is usually available at one of the many University campus colleges. There is also cheaper student accommodation available around the Saint Lucia and Indooroopilly area. Please contact Dr. Steven Holding for all details.

Course Materials

The following items are required: Scientific Calculator (Casio fx82), Technical Drawing Instruments, Protractor, Drawing Compass, 2 mm Graph Paper.

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